Multipass Streaming Algorithms for Regularized Submodular Maximization

In this work,we study a k-Cardinality Constrained Regularized Submodular Maximization(k-CCRSM)problem,in which the objective utility is expressed as the difference between a non-negative submodular and a modular function.No multiplicative approximation algorithm exists for the regularized model,and most works have focused on designing weak approximation algorithms for this problem.In this study,we consider the k-CCRSM problem in a streaming fashion,wherein the elements are assumed to be visited individually and cannot be entirely stored in memory.We propose two multipass streaming algorithms with theoretical guarantees for the above problem,wherein submodular terms are monotonic and nonmonotonic.

A Note on Maximizing Regularized Submodular Functions Under Streaming

Recent progress in maximizing submodular functions with a cardinality constraint through centralized and streaming modes has demonstrated a wide range of applications and also developed comprehensive theoretical guarantees.The submodularity was investigated to capture the diversity and representativeness of the utilities,and the monotonicity has the advantage of improving the coverage.Regularized submodular optimization models were developed in the latest studies(such as a house on fire),which aimed to sieve subsets with constraints to optimize regularized utilities.This study is motivated by the setting in which the input stream is partitioned into several disjoint parts,and each part has a limited size constraint.A first threshold-based bicriteria(1/3,2/3/)-approximation for the problem is provided.

Budget Allocation for Maximizing Viral Advertising in Social Networks

Viral advertising in social networks has arisen as one of the most promising ways to increase brand awareness and product sales. By distributing a limited budget, we can incentivize a set of users as initial adopters so that the advertising can start from the initial adopters and spread via sociM links to become viral. Despite extensive researches in how to target the most influential users, a key issue is often neglected： how to incentivize the initial adopters. In the problem of influence maximization, the assumption is that each user has a fixed cost for being initial adopters, while in practice, user decisions for accepting the budget to be initial adopters are often probabilistic rather than deterministic. In this paper, we study optimal budget allocation in social networks to maximize the spread of viral advertising. In particular, a concave probability model is introduced to characterize each user＇s utility for being an initial adopter. Under this model, we show that it is NP-hard to find an optimal budget allocation for maximizing the spread of viral advertising. We then present a novel discrete greedy algorithm with near optimal performance, and further propose scaling-up techniques to improve the time-efficiency of our algorithm. Extensive experiments on real-world social graphs are implemented to validate the effectiveness of our algorithm in practice. The results show that our algorithm can outperform other intuitive heuristics significantly in almost all cases.